Topological properties of the efficient point set

Abstract

Let y be a closed and convex subset of a Euclidean space. We prove that the set of efficient points of Y, M ( Y ) M(Y) , is contractible. Furthermore, if M ( Y ) M(Y) is closed (compact) then it is a retract of a convex closed (compact) set. Our proof relies on the Arrow-Barankin-Blackwell Theorem. A new proof is supplied for that theorem.